Cavity optomechanics: interactions between light and nanomechanical motion

Transcription

1 Cavity optomechanics: interactions between light and nanomechanical motion Florian Marquardt University of Erlangen-Nuremberg, Germany, and Max-Planck Institute for the Physics of Light (Erlangen) DARPA ORCHID

2 Radiation pressure Johannes Kepler De Cometis, 1619 (Comet Hale-Bopp; by Robert Allevo)

3 Radiation pressure Johannes Kepler De Cometis, 1619

4 Radiation pressure Nichols and Hull, 1901 Lebedev, 1901 Nichols and Hull, Physical Review 13, 307 (1901)

5 Radiation forces Trapping and cooling Optical tweezers Optical lattices...but usually no back-action from motion onto light!

6 Optomechanics on different length scales 4 km Mirror on cantilever Bouwmeester lab, Santa Barbara LIGO Laser Interferometer Gravitational Wave Observatory atoms

7 Optomechanical Hamiltonian laser optical cavity mechanical mode

8 Optomechanical Hamiltonian laser optical cavity mechanical mode

9 Optomechanical Hamiltonian

10 Optomechanical Hamiltonian

11 Optomechanical Hamiltonian...any dielectric moving inside a cavity generates an optomechanical interaction!

12 Basic physics: Statics F rad (x) =2I(x)/c λ 2F λ/2 Experimental proof of static bistability: A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes and H. Walther: Phys. Rev. Lett. 51, 1550 (1983) V rad (x) V eff = V rad + V HO x hysteresis

13 Basic physics: dynamics F quasistatic finite sweep!rate sweep x finite cavity ring-down rate γ delayed response to cantilever motion finite optical ringdown time delayed response to cantilever motion F Fdx < 0 > 0 Höhberger-Metzger and Karrai, Nature 432, 1002 (2004): 300K to 17K [photothermal force] cooling 0 x heating (amplification) C. Höhberger!Metzger and K. Karrai, Nature 432, 1002 (2004) (with photothermal force instead of radiation pressure)

14 The zoo of optomechanical (and analogous) systems Karrai (Munich) Bouwmeester (Santa Barbara) Vahala (Caltech) Kippenberg (EPFL), Carmon,... Harris (Yale) LKB group (Paris) Mavalvala (MIT) Painter (Caltech) Teufel, Lehnert (Boulder) Schwab (Cornell) Stamper-Kurn (Berkeley) cold atoms Aspelmeyer (Vienna)

15 Optomechanics: general outlook Bouwmeester (Santa Barbara/Leiden) Fundamental tests of quantum mechanics in a new regime: entanglement with macroscopic objects, unconventional decoherence? [e.g.: gravitationally induced?] Mechanics as a bus for connecting hybrid components: superconducting qubits, spins, photons, cold atoms,... Kapitulnik lab (Stanford) Tang lab (Yale) Precision measurements [e.g. testing deviations from Newtonian gravity due to extra dimensions] Optomechanical circuits & arrays Exploit nonlinearities for classical and quantum information processing, storage, and amplification; study collective dynamics in arrays

16 Towards the quantum regime of mechanical motion Schwab and Roukes, Physics Today 2005 nano-electro-mechanical systems Superconducting qubit coupled to nanoresonator: Cleland & Martinis 2010 optomechanical systems

17 Optomechanics (Outline) Displacement detection Linear optomechanics Nonlinear dynamics System Bath Quantum theory of cooling Interesting quantum states Towards Fock state detection Hybrid systems: coupling to atoms Optomechanical crystals & arrays

18 Optical displacement detection input laser optical cavity cantilever reflection phase shift

19 Thermal fluctuations of a harmonic oscillator Classical equipartition theorem: Possibilities: extract temperature! Direct time-resolved detection Analyze fluctuation spectrum of x

20 Fluctuation spectrum

21 Fluctuation spectrum

22 Fluctuation-dissipation theorem General relation between noise spectrum and linear response susceptibility susceptibility (classical limit)

23 Fluctuation-dissipation theorem General relation between noise spectrum and linear response susceptibility susceptibility for the damped oscillator: (classical limit)

24 Fluctuation-dissipation theorem General relation between noise spectrum and linear response susceptibility susceptibility for the damped oscillator: (classical limit) area yields variance of x:...yields temperature!

25 Displacement spectrum a n =18 d n =27 m n =71 d n =22 m S x (m 2 /H z) n =280 d n =1,100 d n =8.5 m n =2.9 m n =4,500 d n =0.93 m c Frequency (M H z) Teufel et al., Nature 2011

26 Measurement noise

27 Measurement noise meas Two contributions to phase noise of 1. measurement imprecisionlaser beam (shot noise limit!) 2. measurement back-action: fluctuating force on system noisy radiation pressure force

28 Standard Quantum Limit full noise (including back-action) imprecision noise intrinsic (thermal & quantum) noise measured noise (log scale) imprecision noise SQL zero-point fluctuations back-action noise laser power (log scale) Best case allowed by quantum mechanics: Standard quantum limit (SQL) of displacement detection...as if adding the zero-point fluctuations a second time: adding half a photon

29 Notes on the SQL weak measurement : integrating the signal over time to suppress the noise trying to detect slowly varying quadratures of motion : Heisenberg is the reason for SQL! no limit for instantaneous measurement of x(t)! SQL means: detect down to on a time scale Impressive:!

30 Optomechanics (Outline) Displacement detection Linear optomechanics Nonlinear dynamics System Bath Quantum theory of cooling Interesting quantum states Towards Fock state detection Hybrid systems: coupling to atoms Optomechanical crystals & arrays

31 Equations of motion cantilever input laser optical cavity

32 Equations of motion cantilever input laser optical cavity mechanical frequency mechanical damping equilibrium position radiation pressure detuning from resonance cavity decay rate laser amplitude

33 Linearized optomechanics (solve for arbitrary ) Optomechanical frequency shift ( optical spring ) Effective optomechanical damping rate

34 Linearized dynamics Effective optomechanical damping rate Optomechanical frequency shift ( optical spring ) laser detuning cooling heating/ amplification softer stiffer

35 Linearized dynamics Effective optomechanical damping rate Optomechanical frequency shift ( optical spring ) laser detuning cooling heating/ amplification softer stiffer

36 Optomechanics (Outline) Displacement detection Linear optomechanics Nonlinear dynamics System Bath Quantum theory of cooling Interesting quantum states Towards Fock state detection Hybrid systems: coupling to atoms Optomechanical crystals & arrays

37 Self-induced oscillations F Fdx < 0 > 0 x total

38 Self-induced oscillations F Fdx < 0 > 0 x total Beyond some laser input power threshold: instability Cantilever displacement x Time t Amplitude A

39 Attractor diagram power fed into the cantilever 1 0 cantilever energy detuning FM, Harris, Girvin, PRL 96, (2006) Ludwig, Kubala, FM, NJP 2008

40 Attractor diagram power fed into the cantilever 1 power balance 0 cantilever energy detuning FM, Harris, Girvin, PRL 96, (2006) Ludwig, Kubala, FM, NJP 2008

41 Attractor diagram power fed into the cantilever 1 power balance 0 cantilever energy detuning FM, Harris, Girvin, PRL 96, (2006) Ludwig, Kubala, FM, NJP 2008

42 Optomechanics (Outline) Displacement detection Linear optomechanics Nonlinear dynamics System Bath Quantum theory of cooling Interesting quantum states Towards Fock state detection Hybrid systems: coupling to atoms Optomechanical crystals & arrays

43 Cooling with light input laser optical cavity cantilever Current goal in the field: ground state of mechanical motion of a macroscopic cantilever Classical theory: Pioneering theory and experiments: Braginsky (since 1960s ) optomechanical damping rate

44 Cooling with light input laser optical cavity cantilever Current goal in the field: ground state of mechanical motion of a macroscopic cantilever Classical theory: quantum limit? Pioneering theory and experiments: Braginsky (since 1960s ) shot noise! optomechanical damping rate

45 Cooling with light input laser optical cavity cantilever Quantum picture: Raman scattering sideband cooling Original idea: Sideband cooling in ion traps Hänsch, Schawlow / Wineland, Dehmelt 1975 Similar ideas proposed for nanomechanics: cantilever + quantum dot Wilson-Rae, Zoller, Imamoglu 2004 cantilever + Cooper-pair box Martin Shnirman, Tian, Zoller 2004 cantilever + ion Tian, Zoller 2004 cantilever + supercond. SET Clerk, Bennett / Blencowe, Imbers, Armour 2005, Naik et al. (Schwab group) 2006

46 phonon number LKB MIT Laser-cooling towards the ground state 1x x10 9 1x10 8 1x10 7 1x ground state Yale IQOQI MPQ minimum possible phonon number JILA Caltech 2011 Boulder 2011 analogy to (cavity-assisted) laser cooling of atoms FM et al., PRL 93, (2007) Wilson-Rae et al., PRL 99, (2007)

47 Optomechanics (Outline) Displacement detection Linear optomechanics Nonlinear dynamics System Bath Quantum theory of cooling Interesting quantum states Towards Fock state detection Hybrid systems: coupling to atoms Optomechanical crystals & arrays

48 Squeezed states Squeezing the mechanical oscillator state

49 Squeezed states Squeezing the mechanical oscillator state

50 Squeezed states Squeezing the mechanical oscillator state

51 Squeezed states Squeezing the mechanical oscillator state t x

52 Squeezed states Squeezing the mechanical oscillator state t x Periodic modulation of spring constant: Parametric amplification

53 Squeezed states Squeezing the mechanical oscillator state t x Periodic modulation of spring constant: Parametric amplification

54 Squeezed states Squeezing the mechanical oscillator state t x Periodic modulation of spring constant: Parametric amplification

55 Squeezed states Squeezing the mechanical oscillator state t x Periodic modulation of spring constant: Parametric amplification

56 Measuring quadratures ( beating the SQL ) amplitude-modulated input field (similar to stroboscopic measurement) Clerk, Marquardt, Jacobs; NJP 10, (2008) measure only one quadrature, back-action noise affects only the other one...need:

57 Measuring quadratures ( beating the SQL ) amplitude-modulated input field (similar to stroboscopic measurement) Clerk, Marquardt, Jacobs; NJP 10, (2008) measure only one quadrature, back-action noise affects only the other one...need: p reconstruct mechanical Wigner density (quantum state tomography) x

58 Measuring quadratures ( beating the SQL ) amplitude-modulated input field (similar to stroboscopic measurement) Clerk, Marquardt, Jacobs; NJP 10, (2008) measure only one quadrature, back-action noise affects only the other one...need: p reconstruct mechanical Wigner density (quantum state tomography) x

59 Measuring quadratures ( beating the SQL ) amplitude-modulated input field (similar to stroboscopic measurement) Clerk, Marquardt, Jacobs; NJP 10, (2008) measure only one quadrature, back-action noise affects only the other one...need: p reconstruct mechanical Wigner density (quantum state tomography) x

60 Optomechanical entanglement Bose, Jacobs, Knight 1997; Mancini et al. 1997

61 Optomechanical entanglement Bose, Jacobs, Knight 1997; Mancini et al. 1997

62 Optomechanical entanglement n=0 n=1 n=2 n=3 entangled state (light field/mechanics) coherent mechanical state Bose, Jacobs, Knight 1997; Mancini et al. 1997

63 Proposed optomechanical which-path experiment and quantum eraser p x Recover photon coherence if interaction time equals a multiple of the mechanical period! cf. Haroche experiments in 90s Marshall, Simon, Penrose, Bouwmeester, PRL 91, (2003)

64 Optomechanics (Outline) Displacement detection Linear optomechanics Nonlinear dynamics System Bath Quantum theory of cooling Interesting quantum states Towards Fock state detection Hybrid systems: coupling to atoms Optomechanical crystals & arrays

65 Membrane in the middle setup optical frequency Thompson, Zwickl, Jayich, Marquardt, Girvin, Harris, Nature 72, 452 (2008)

66 Membrane in the middle setup optical frequency Thompson, Zwickl, Jayich, Marquardt, Girvin, Harris, Nature 72, 452 (2008) frequency membrane transmission membrane displacement

67 Experiment (Harris group, Yale) Mechanical frequency: ωm=2π 134 khz Mechanical quality factor: Q= nm SiN membrane Current optical finesse: ( ) [almost sideband regime] Optomechanical cooling from 300K to 7mK Thompson, Zwickl, Jayich, Marquardt, Girvin, Harris, Nature 72, 452 (2008)

68 Towards Fock state detection of a macroscopic object Detection of displacement x: not what we need!

69 Towards Fock state detection of a macroscopic object Detection of displacement x: not what we need! frequency membrane transmission membrane displacement

70 Towards Fock state detection of a macroscopic object Detection of displacement x: not what we need! frequency membrane transmission membrane displacement

71 Towards Fock state detection of a macroscopic object frequency membrane transmission membrane displacement phase shift of measurement beam:

72 Towards Fock state detection of a macroscopic object frequency membrane transmission membrane displacement phase shift of measurement beam: (Time-average over cavity ring-down time) QND measurement of phonon number!

73 Towards Fock state detection of a macroscopic object simulated phase shift (phonon number) Time Thompson, Zwickl, Jayich, FM, Girvin, Harris, Nature 72, 452 (2008)

74 Towards Fock state detection of a macroscopic object simulated phase shift (phonon number) Time Thompson, Zwickl, Jayich, FM, Girvin, Harris, Nature 72, 452 (2008)

75 Towards Fock state detection of a macroscopic object simulated phase shift (phonon number) Time Thompson, Zwickl, Jayich, FM, Girvin, Harris, Nature 72, 452 (2008)

76 Towards Fock state detection of a macroscopic object simulated phase shift (phonon number) Time Thompson, Zwickl, Jayich, FM, Girvin, Harris, Nature 72, 452 (2008)

77 Towards Fock state detection of a macroscopic object Signal-to-noise ratio: simulated phase shift (phonon number) Optical freq. shift per phonon: Noise power of freq. measurement: Ground state lifetime: Time Thompson, Zwickl, Jayich, FM, Girvin, Harris, Nature 72, 452 (2008)

78 Towards Fock state detection of a macroscopic object Signal-to-noise ratio: simulated phase shift (phonon number) very challenging! Optical freq. shift per phonon: Noise power of freq. measurement: Ground state lifetime: Time Thompson, Zwickl, Jayich, FM, Girvin, Harris, Nature 72, 452 (2008)

79 Optomechanics (Outline) Displacement detection Linear optomechanics Nonlinear dynamics System Bath Quantum theory of cooling Interesting quantum states Towards Fock state detection Hybrid systems: coupling to atoms Optomechanical crystals & arrays

80 Atom-membrane coupling Note: Existing works simulate optomechanical effects using cold atoms K. W. Murch, K. L. Moore, S. Gupta, and D. M. Stamper-Kurn, Nature Phys. 4, 561 (2008). F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, Science 322, 235 (2008). Stamper-Kurn (Berkeley) cold atoms...profit from small mass of atomic cloud Here: Coupling a single atom to a macroscopic mechanical object Challenge: huge mass ratio

81 Strong atom-membrane coupling via the light field existing experiments on optomechanics with cold atoms : labs of Dan-Stamper Kurn (Berkeley) and Tilman Esslinger (ETH) collaboration: LMU (M. Ludwig, FM, P. Treutlein), Innsbruck (K. Hammerer, C. Genes, M. Wallquist, P. Zoller), Boulder (J. Ye), Caltech (H. J. Kimble) Hammerer et al., PRL 2009 Goal: atom membrane atom-membrane coupling

82 Optomechanics (Outline) Displacement detection Linear optomechanics Nonlinear dynamics System Bath Quantum theory of cooling Interesting quantum states Towards Fock state detection Hybrid systems: coupling to atoms Optomechanical crystals & arrays

83 Many modes 8 mechanical mode optical mode

84 Scaling down cm usual optical cavities 10 µm LKB, Aspelmeyer, Harris, Bouwmeester,...

85 Scaling down cm usual optical cavities 50 µm 10 µm LKB, Aspelmeyer, Harris, Bouwmeester,... microtoroids Vahala, Kippenberg, Carmon,...

86 Scaling down cm usual optical cavities 50 µm 10 µm LKB, Aspelmeyer, Harris, Bouwmeester,... microtoroids optomechanics in photonic circuits Vahala, Kippenberg, Carmon,... optomechanical crystals 5 µm H. Tang et al., Yale O. Painter et al., Caltech 10 µm

87 Optomechanical crystals free-standing photonic crystal structures optical modes advantages: tight vibrational confinement: high frequencies, small mass (stronger quantum effects) vibrational modes tight optical confinement: large optomechanical coupling (100 GHz/nm) integrated on a chip from: M. Eichenfield et al., Optics Express 17, (2009), Painter group, Caltech

88 Optomechanical arrays laser drive cell 1 cell 2 optical mode mechanical mode... collective nonlinear dynamics: classical / quantum cf. Josephson arrays

89 Dynamics in optomechanical arrays Outlook 2D geometries Quantum or classical information processing and storage (continuous variables) Dissipative quantum many-body dynamics (quantum simulations) Hybrid devices: interfacing GHz qubits with light

90 Photon-phonon translator (concept: Painter group, Caltech) strong optical pump 1 phonon photon 2

91 Superconducting qubit coupled to nanomechanical resonator Josephson phase qubit 2010: Celand & Martinis labs piezoelectric nanomechanical resonator 20 mk: ground state!) swap excitation between qubit and mechanical resonator in a few ns!

92 Conversion of quantum information phonon-photon translation Josephson phase qubit nanomechanical resonator light

93 Recent trends Ground-state cooling: success! (spring 2011) [Teufel et al. in microwave circuit; Painter group in optical regime] Optomechanical (photonic) crystals Multiple mechanical/optical modes Option: build arrays or optomechanical circuits Strong improvements in coupling Possibly soon: ultrastrong coupling (resolve single photonphonon coupling) Hybrid systems: Convert GHz quantum information (superconducting qubit) to photons Hybrid systems: atom/mechanics [e.g. Treutlein group] Levitating spheres: weak decoherence! [Barker/ Chang et al./ Romero-Isart et al.]

94 Optomechanics: general outlook Bouwmeester (Santa Barbara/Leiden) Fundamental tests of quantum mechanics in a new regime: entanglement with macroscopic objects, unconventional decoherence? [e.g.: gravitationally induced?] Mechanics as a bus for connecting hybrid components: superconducting qubits, spins, photons, cold atoms,... Kapitulnik lab (Stanford) Tang lab (Yale) Precision measurements [e.g. testing deviations from Newtonian gravity due to extra dimensions] Optomechanical circuits & arrays Exploit nonlinearities for classical and quantum information processing, storage, and amplification; study collective dynamics in arrays

95 Optomechanics Recent review on optomechanics: APS Physics 2, 40 (2009) Recent review on quantum limits for detection and amplification: Clerk, Devoret, Girvin, Marquardt, Schoelkopf; RMP 2010